18/7 + 13/18 as a fraction

Learn how to find what is 18/7 plus 13/18 in fraction form just in a few minutes. We have covered the easiest method to write 18/7 + 13/18 as a fraction and decimal.

Summary: 18/7 plus 13/18 = 415/126
Since both fractions have unequal denominators, 18/7 plus 13/18 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 18/7 and fraction 13/18 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 18. 126 is the LCM of 7 and 18. Multiplying the LCM 126 with the numerators and denominators of both fractions (18/7 x 126/126) + (13/18 x 126/126), and simplify further in order to have the common denominator. So the equivalent fraction for 18/7 is 324/126 and for 13/18 is 91/126. By simplifying this fraction addition 324/126 + 91/126, it becomes 415/126.

CALCULATION: 18/7 + 13/18 as a fraction
18/7 + 13/18 = (?)
18/7 + 13/18 = [(18 x 18) + (13 x 7)]/(7 x 18)
= (324 + 91)/126
= 415/126
18/7 + 13/18 = 415/126
18/7 plus 13/18 as a fraction is 415/126.

where
18/7 is a improper fraction as an addend,
13/18 is a proper fraction as an addend,
415/126 is the sum of 18/7 and 13/18.

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18/7 plus 13/18 as a decimal
18/7 + 13/18 = 415/126
415/126 = 3.2937
(18/7) + (13/18) as a decimal is 3.2937

where
3.2937 is the sum of 18/7 and 13/18.

The below workout with step by step calculation shows how to find the equivalent fraction between 18/7 and 13/18 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 18/7 plus 13/18 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(18/7) + (13/18) using LCM Method:
What is 18/7 plus 13/18 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/7
Fraction B: 13/18

What to be found?
(18/7) + (13/18) = ?
Find what's the sum of 18/7 and 13/18.

step 2 Compare the denominators of fractions 18/7 and 13/18 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 18/7 and 13/18 are not equal, it is said to be unlike fractions addition.

step 3For unlike fractions addition, find the LCM (least common multiple) of both denominators of fractions 18/7 and 13/18:
The LCM of 7 and 18 is 126.

step 4 Write the fractions 18/7 and 13/18 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 18/7 + 13/18
= [(18 x 126)/(7 x 126)] + [(13 x 126)/(18 x 126)]

step 5 Simplify the expression to have common denominator:
= 324/126 + 91/126

step 6 Take the common values out and rewrite the above expression like the below:
= 1/126 x (324/1 + 91/1)
= 1/126 x (324 + 91)

step 7Simplify the above expression further:
= 1/126 x 415
= 415/126
18/7 + 13/18 = 415/126

Hence,
18/7 plus 13/18 as a fraction is 415/126.

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18/7 + 13/18 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/7
Fraction B: 13/18

What to be found?
(18/7)+(13/18) = ?
Find what's the sum of 18/7 and 13/18.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (18 x 18), find the product of numerator of Fraction B and denominator of Fraction A (13 x 7), and find the product of both denominators of Fraction A and Fraction B (7 x 18) and rewrite the equation as like the below:
= (18 x 18) + (13 x 7)/(7 x 18)

step 3 Simplify and rewrite the fraction:
= (324 + 91)/126
18/7 + 13/18 = 415/126

Hence,
18/7 plus 13/18 in fraction is 415/126